The Lesson

The greatest common factor is the largest factor that is common to two or more numbers.

Understanding the Greatest Common Factor

The numbers that multiply together to make another number are its factors. 2 is a factor of 4 because 2 × 2 = 4:

4 = 2 times 2 2 and 3 are factors of 6 because 2 × 3 = 6:

6 = 2 times 3 The greatest common factor is the largest number that is a factor for both numbers. In our example, 2 is the greatest common factor.

2 is the greatest common factor of 4 and 6 Another way of thinking about a factor is as a number which divides exactly into another number. 2 is the largest number that divides exactly into 4 and 6.
4 ÷ 2 = 2 6 ÷ 2 = 3

What's in a Name?

The Greatest Common Factor (GCF) is so called because it is the largest (greatest) factor that is the same (common) to the numbers. It may sometimes be called:
  • Greatest Common Divisor (GCD)
  • Highest Common Factor (HCF)

Finding the Greatest Common Factor of More than Two Numbers

In the examples here, the greatest common factor has been been found for two numbers. But the same procedure extends to any number of numbers.